Method of judging practical conditions for use of an ordered alloy under irradiation environments

ABSTRACT

An irradiated state diagram that expresses a relation of the degree of long range order to a variable R of an irradiated state related to a damage rate and an irradiation temperature is prepared according to an ordered structure of an alloy on the basis of an evaluation formula related to the effect of irradiation on an irradiated state of the alloy by using, as parameters, the first threshold value at which the degree of long range order begins to decrease greatly under irradiation, the second threshold value at which the degree of long range order almost reaches equilibrium after the decrease, and the degree of long range order in an equilibrium state. A variable R of an irradiated state under irradiation conditions under which an alloy to be judged is to be used is calculated and an S-value of degree of long range order corresponding to the variable R is found. The first threshold value, the second threshold value and the degree of long range order in an equilibrium state at the same R-value are found and compared, to thereby predict a damage level and a variation condition of the damage level and judge the practical conditions for use. According to the present invention, it is possible to judge the practical conditions for use of the materials under irradiation in a short period and at low cost, in pursuing the application of new materials represented by an ordered alloy to irradiation environments.

FIELD OF THE INVENTION

The present invention relates to a method of judging the practicalconditions for use of an ordered alloy (in this specification, the“alloy” is used as a term including an alloy and an intermetalliccompound) having an ordered structure in irradiation environments. Thistechnique is useful for deriving the practical conditions for use ofelement equipment or structures formed from ordered alloys inenvironments in which materials used are exposed to radiation havinghigh energy, for example, in the nuclear technology field such asreactors and accelerators and the space technology field.

BACKGROUND OF THE INVENTION

In using new materials in irradiation environments in which high-energycorpuscular beams are emitted and the occurrence of severe irradiationdamage is expected, it is necessary to evaluate beforehand the usabilityand long-period soundness of the materials in the environments. Hence,in prior art, an irradiation test plan in which the environments aresimulated is first formulated, irradiation experiments in which manyirradiation conditions are parameterized are conducted, and obtainedsystematic post-irradiation examination (PIE) data is analyzed tothereby obtain practical conditions in which the materials can be usedunder irradiation.

However, in order to conduct a high-accuracy evaluation analysis thatcan ensure high safety and reliability during use of the materials, along period and much cost for an enormous number of tests and asufficient analysis are required. For example, in the development ofmaterials for fission reactors in the study of light-water reactors andhigh-temperature gas reactors and the development of materials fornuclear fusion reactors, in a case where new materials that have noirradiation result are used in irradiation environments, the developmentof new materials represented by Zircaloy, Hastelloy XR, austeniticstainless steels, fine-grained isotropic graphite, etc. has required adevelopment period of the order of 10 years and an enormous developmentcost have been indispensable.

Therefore, as described in the following Reports 1-4 etc., there havebeen available methods by which multiple research institutes storeenormous irradiation data in collaboration by assembling an irradiationdatabase on materials and use the data in analyses. Under presentcircumstances, however, such methods have not yet reached a stage atwhich irradiation data can be systematically analyzed, and there is noanalysis solution, calculation code or data base capable of easilyderiving practical conditions for use.

A description of irradiation damage to materials is very complex.Irradiation damage starts with the collision of high-energy particlesand is composed of the instantaneous heating and cooling processes andvarious reaction processes, such as atomic displacement, generation,growth and diffusion of defects, aggregation and coalescence of defects,initiation and propagation of cracks. Although part of these reactionsare expressed by mathematical formulae such as a diffusion equation,almost all of these reactions require high-speed and large-capacityprocessing by a computer on the basis of statistical processing bymolecular dynamics, the Monte Carlo method and dislocation dynamics. Forthis reason, because at present there is a limit to the calculatingperformance of computers, it is difficult to analyze the whole pictureof irradiation damage and to systematically grasp the irradiation damageeven if a next-generation super computer is used. Furthermore, there isno evaluation formula that enables a description of irradiation damageto be reflected in an evaluation of the material characteristics and,therefore, it has hitherto been impossible to instantaneously derivepractical conditions under which materials can be used under irradiation(practical conditions for use).

The problem to be solved in the present invention is that in pursuingthe application of new materials represented by ordered alloys toirradiation environments, there is no method of judging the practicalconditions for use of the materials under irradiation in a short periodand at low cost and that for this reason, it has been difficult tointroduce materials that have no irradiation result.

Report 1: Shuichi Iwata et al., Materials Data Base for FusionReactors-1, Journal of Nuclear Materials, Vol. 103 (1982), pp. 173-177.

Report 2: Hajime Nakajima et al., Present status ofData-Free-Way—Distributed database for advanced nuclear materials,Journal of Nuclear Materials, Vol. 212/215 (1994), pp. 1711-1714.

Report 3: Mitsutane Fujita et al., Application of the distributeddatabase (Data-Free-Way) on the analysis of mechanical properties inneutron irradiated 316 stainless steel, Fusion Engineering and Design,Vol. 51/52 (2000), pp. 769-774.

Report 4: Yoshiyuki Kaji et al., Status of JAERI Material PerformanceDatabase (JMPD) and Analysis of Irradiation Assisted Stress CorrosionCracking (IASCC) Data, Journal of Nuclear Science and Technology, Vol.37 (2000), pp. 949-958.

SUMMARY OF THE INVENTION

According to the present invention, there is provided a method by whichirradiation behavior is assumed to be caused by the generation andannihilation of irradiation defects, an index that expresses anirradiated state is used, an evaluation formula in which the effect ofirradiation environments on the index is considered is derived on thebasis of the index, and changes in the index due to the effect ofirradiation and the conditions of the irradiation environments on thatoccasion are simply and rapidly predicted.

More specifically, according to the present invention there is provideda method of judging practical conditions for use of an ordered alloy inirradiation environments, comprising the steps of: preparing anirradiated state diagram that expresses a relation of a degree of longrange order to a variable R of an irradiated state related to a damagerate, which can be obtained from fluence rate, and an irradiationtemperature on the basis of an evaluation formula related to the effectof irradiation on an irradiated state of an alloy according to anordered structure of the alloy by using, as parameters, the firstthreshold value at which the degree of long range order begins todecrease greatly under irradiation, the second threshold value at whichthe degree of long range order almost reaches equilibrium after thedecrease, and the degree of long range order in an equilibrium state;calculating a variable R of an irradiated state under irradiationconditions under which an alloy to be judged is to be used and findingan S-value of degree of long range order corresponding to the variableR; and finding and comparing the first threshold value S_(th1), thesecond threshold value S_(th2) and the degree of long range order in anequilibrium state S_(eq) at the same R-value, to thereby predict adamage level and a variation condition of the damage level and judge thepractical conditions for use.

Also, according to the present invention there is provided a method ofjudging practical conditions for use of ordered alloy in irradiationenvironments, comprising the steps of: preparing an irradiated statediagram that expresses a relation of a damage rate (fluence rate) to areciprocal of an irradiation temperature on the basis of an evaluationformula related to the effect of irradiation on an irradiated state ofan alloy according to an ordered structure of the alloy by using, asparameters, the first threshold value at which the degree of long rangeorder begins to decrease greatly under irradiation, the second thresholdvalue at which the degree of long range order almost reaches equilibriumafter the decrease, and the degree of long range order in an equilibriumstate; calculating a reciprocal of an irradiation temperature of analloy to be judged under irradiation conditions under which the alloy isto be used and finding an S-value of degree of long range ordercorresponding to the reciprocal of the irradiation temperature; andfinding and comparing the first threshold value S_(th1), the secondthreshold value S_(th2) and the degree of long range order in anequilibrium state S_(eq) at the same reciprocal of the irradiationtemperature, to thereby predict a damage level and a variation conditionof the damage level and judge the practical conditions for use.

In these judgment methods, a comparison is made between the S-value andthe S_(th1)-value, the S_(th2)-value and the S_(eq)-value, respectively,at the same R-value or the same reciprocal of an irradiation temperature(where, 0≦S_(eq)<S_(th2)<S_(th1)<1), and from a magnitude relation ofthese values judgments can be made as follows:

-   (1) When S_(th1)<S: the alloy to be judged is in an ordered state    and has a low damage level (the degree of long range order is    large);-   (2) When S_(th2)<S<S_(th1): the alloy to be judged is in a    transition process from an ordered state to a disordered state and    its damage level fluctuates greatly and tends to increase rapidly    (the degree of long range order decreases substantially);-   (3) When S_(eq)<S<S_(th2): the alloy to be judged is in a process of    almost reaching a disordered state and its damage level is large but    little fluctuates (the amount of a decrease in the degree of long    range order is small and the degree of long range order is small)    and;-   (4) When S<S_(eq): the alloy to be judged is in a disordered state    and has a high damage level (the degree of long range order is    small).

According to the present invention, it is possible to substantiallysimplify a large number of irradiation experiments that have hithertobeen necessary and to simply and rapidly derive practical conditions foruse of an ordered alloy (an alloy with an ordered structure) underirradiation, such as irradiation temperature, damage rate (fluence rate)and irradiation fluence, without the need for assembling a newirradiation database. For this reason, it is possible to substantiallyshorten the periods of enormous irradiation tests, post-irradiationexaminations (PIE) and analysis evaluations, long-period implementationof which has hitherto been indispensable, and it is possible toradically reduce prior-irradiation test expenses, irradiation testexpenses, post-irradiation examination expenses, analysis expenses, etc.As a result of this, it is possible to rapidly and efficiently promotethe development of new materials that are resistant to irradiationenvironments, such as an ordered alloy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a relation diagram of degree of long range order (degree ofshort range order) and R-value of a B2-type ordered alloy; and

FIG. 2 is a relation diagram of damage rate and irradiation temperatureof a B2-type ordered alloy.

PREFERRED EMBODIMENTS OF THE INVENTION

In the present invention, an evaluation formula based on order-disordertransition under irradiation is used. Atomic replacement generated byirradiation induces a local structural change in an ordered alloy, andthe ordered alloy is disordered under irradiation. On the other hand,the introduction of irradiation defects is promoted with an irradiationtemperature and the ordering of the ordered alloy is promoted. Anirradiated state of the ordered alloy is a process in which suchdisordering and ordering proceed simultaneously, and under theconditions in which disordering and ordering are balanced, thisirradiated state is greatly influenced by variations in irradiationtemperature, damage rate (fluence rate) and irradiation fluence thatconstitute irradiation environment conditions.

Hence, by paying attention to a degree of long range order of an orderedalloy as an index that expresses an irradiated state that reflects aneffect of irradiation, an influence of irradiation on the degree of longrange order is analyzed and an evaluation formula in which the effect ofirradiation on the degree of long range order is considered is derived.“The degree of order” used herein is a physical quantity that expressesthe kind of atomistic quantity having order and the degree of this orderin the order-disorder transition, and this is a parameter that featuresphase transition. A relationship between an irradiation temperature anda damage rate corresponding to a threshold value of the effect ofirradiation is found by this evaluation equation and a diagram for theanalysis of an irradiated state is prepared. When this diagram for eachordered alloy is prepared, the conditions of damage rate and irradiationtemperature that can be used under irradiation become apparent easily.

Typically, an irradiated state diagram that expresses a relation of thedegree of long range order to a variable R of an irradiated staterelated to a damage rate and an irradiation temperature is preparedaccording to an ordered structure of an alloy on the basis of anevaluation formula related to the effect of irradiation on an irradiatedstate of the alloy by using, as parameters, the first threshold value atwhich the degree of long range order begins to decrease greatly underirradiation, the second threshold value at which the degree of longrange order almost reaches equilibrium after the decrease, and thedegree of long range order in an equilibrium state. On the other hand, avariable R of an irradiated state under irradiation conditions underwhich an alloy to be judged is to be used is calculated and an S-valueof degree of long range order corresponding to the variable R is found.At the same time, the first threshold value S_(th1), the secondthreshold value S_(th2) and the degree of long range order in anequilibrium state S_(eq) at the same R-value are found and compared.

A comparison is made between the S-value and the S_(th1)-value, theS_(th2)-value and the S_(eq)-value, respectively, at the same R-value(where, 0≦S_(eq)<S_(th2)<S_(th1)<1), and from a magnitude relation ofthese values judgments can be made as follows:

-   (1) When S_(th1)<S: the alloy is in an ordered state and has a low    damage level (the degree of long range order is large);-   (2) When S_(th2)<S<S_(th1): the alloy is in a transition process    from an ordered state to a disordered state and its damage level    fluctuates greatly and tends to increase rapidly (the degree of long    range order decreases substantially);-   (3) When S_(eq)<S<S_(th2): the alloy is in a process of almost    reaching a disordered state and its damage level is large but little    fluctuates (the amount of a decrease in the degree of long range    order is small and the degree of long range order is small) and;-   (4) When S<S_(eq): the alloy is in a disordered state and has a high    damage level (the degree of long range order is small). In this    manner, a damage level and a variation condition of the damage level    are predicted and the practical conditions for use are judged.

EXAMPLE

An irradiated state depends greatly on irradiation temperature,irradiation damage and damage rate that constitute irradiationenvironments. Damage rates under irradiation conditions in JapanMaterials Testing Reactor (JMTR) of Japan Atomic Energy ResearchInstitute are 10⁻⁷ to 10⁻⁸ dpa/s and damage rates under irradiationconditions in Experimental Fast Reactor (JOYO) of Japan Nuclear CycleDevelopment Institute are 10⁻⁶ to 10⁻⁸ dpa/s. The temperatures at whichdamage of the ordered alloy irradiated in these testing reactors isrecovered are derived by making a comparison between irradiationenvironment conditions and threshold values in an irradiated statediagram according to the present invention and an irradiated state canbe judged on the basis of the temperatures.

Derivation of an evaluation formula related to an irradiation effect isperformed as follows. A case of a B2-type ordered alloy (a CsCl-typeordered alloy, the composition ratio of the number of A atoms to thenumber of B atoms is 1:1, A atoms and B atoms constituting a binaryalloy), which is a representative ordered alloy, is illustrated here byan example. However, also cases of other ordered alloys can be similarlyhandled. The same applies also when the degree of short range order byWarren-Cowley or the like is used in place of the degree of long rangeorder (the degree of long range order of Bragg-Williams). The degree oflong range order (the degree of long range order of Bragg-Williams) S ofa B2-type ordered alloy under irradiation is defined by S=(theprobability that composed sublattices are correctly occupied byconstituent atoms)−(the probability that composed sublattices are notcorrectly occupied by constituent atoms). That is, $\begin{matrix}{S = {\frac{C_{A}^{\alpha} - C_{A}}{1 - C_{A}} = \frac{C_{B}^{\beta} - C_{B}}{1 - C_{B}}}} \\( {{0 \leq S \leq 1},{{C_{A} + C_{B}} = 1}} )\end{matrix}$where, α and β denote an α sublattice and a β sublattice, respectively,in the ordered alloy and the subscripts A and B denote an A atom and a Batom, respectively. The rate of time change of this degree of long rangeorder is given by: $\begin{matrix}{\frac{\mathbb{d}S}{\mathbb{d}t} = {\lbrack \frac{\mathbb{d}S}{\mathbb{d}t} \rbrack_{disordering} + \lbrack \frac{\mathbb{d}S}{\mathbb{d}t} \rbrack_{ordering}}} \\{= {{{- ɛ}\quad\phi\quad S} + {K( {1 - S} )}^{2}}}\end{matrix}$where, the former term of the right side denotes a disordering rate andthe latter term denotes an ordering rate.

In the present specification, symbols in formulae are as follows:

-   ε: Efficiency of disordering-   φ: Damage rate-   K: Function of temperature    $K = {( {Z_{\alpha} + Z_{\beta} - 2} )\quad{c_{v} \cdot v \cdot c_{A}}c_{B}\quad{\exp( {- \frac{E}{kT}} )}}$-   Z_(α), Z_(β): Coordination number of α sublattices and β sublattices-   Cv: Vacancy concentration (assumed to be proportional to the ½-th    power of the damage rate)-   ν: Frequency factor-   C_(A), C_(B): Concentration of A atoms and B atoms-   E: Activation energy for the ordering jump of vacancy-   κ: Boltzmann constant-   T: Temperature

The following equation is obtained from the balance conditions of theordering process and disordering process in irradiation environments:$\frac{\mathbb{d}S}{\mathbb{d}t} = {{{- ɛ}\quad\phi\{ {S - {R( {1 - S} )}^{2}} \}} = {{ɛ\quad\phi\quad{R( {S - \alpha} )}\quad( {S - \beta} )} = 0}}$where, the two roots of α and β are given by:$\alpha,{\beta = {\frac{{2R} + 1}{2R} \pm \sqrt{\frac{{4R} + 1}{4R^{2}}}}}$(A plus or minus sign should be chosen in the double sign, β<α, 0<β<1,1<α)A solution is obtained only for S=β that satisfies 0≦S<1.However, R=κ/εφ=S_(eq)/(1−S_(eq))²(0≦R<∞)where, S_(eq) denotes the degree of long range order in an equilibriumstate.

Therefore, the following analytic solution using R as a parameter isobtained: $\begin{matrix}{S = {\beta + \frac{( {\alpha - \beta} )\quad( {1 - \beta} )}{{( {\alpha - 1} )\quad\exp\{ {ɛ\quad{R( {\alpha - \beta} )}\phi\quad t} \}} + ( {1 - \beta} )}}} & ( {{Equation}\quad 1} )\end{matrix}$

The degree of long range order S decreases gradually from a value beforeirradiation (S=1) with increasing irradiation time due to irradiationand reaches an equilibrium value in a certain irradiation time. Theformer term β in the equation is the degree of long range order in anequilibrium state S_(eq) corresponding to a convergent value at thistime. The latter term is a time dependent term and shows details of timevariations in the degree of long range order that gradually approximatesthe degree of long range order in an equilibrium state with increasingirradiation time.

The relationship between the first threshold value S_(th1) at which thedegree of long range order S begins to decrease greatly underirradiation, the second threshold value S_(th2) at which the degree oflong range order almost reaches equilibrium after the decrease, and theparameter R is given by the following equations from results ofsecondary differential and primary differential related to R:$\begin{matrix}\begin{matrix}{S_{th1} = {1 + {\frac{1}{2R}\{ {1 - \frac{( {{4R} + 1} )^{2}}{{( {{2R} + 1} )\quad( {{4R} + 1} )} + {4R^{2}}}} \}}}} \\{= {1 + {\frac{ɛ\quad\phi}{2K}\{ {1 - \frac{( {{4K} + {ɛ\quad\phi}} )^{2}}{{( {{2K} + {ɛ\quad\phi}} ) \cdot ( {{4K} + {ɛ\quad\phi}} )} + {4\quad K^{2}}}} \}}}}\end{matrix} & ( {{Equation}\quad 2} ) \\{S_{th2} = {\frac{2R}{{2R} + 1} = \frac{2K}{{2K} + {ɛ\quad\phi}}}} & ( {{Equation}\quad 3} )\end{matrix}$Furthermore, the degree of long range order in an equilibrium stateS_(eq) is found by the following equation: $\begin{matrix}\begin{matrix}{S_{eq} = {1 + {\frac{1}{2R}\{ {1 - ( {{4R} + 1} )^{\frac{1}{2}}} \}}}} \\{= {1 + {\frac{( {ɛ\quad\phi} )^{\frac{1}{2}}}{2K}\{ {( {ɛ\quad\phi} )^{\frac{1}{2}} - ( {{4K} + {ɛ\quad\phi}} )^{\frac{1}{2}}} \}}}} \\{= {\frac{1}{2K}\lbrack {{2K} + {ɛ\quad\phi} - \{ {ɛ\quad{\phi( {{4K} + {ɛ\quad\phi}} )}} \}^{\frac{1}{2}}} \rbrack}} \\{{where},{0 \leq S_{eq} < S_{th2} < S_{th1} < 1.}}\end{matrix} & ( {{Equation}\quad 4} )\end{matrix}$

On the other hand, the degrees of short range order of Warren-Cowley σcorresponding to each of the degrees of long range order are found asfollows. The number of A-A atom pairs formed by A atoms in a binaryalloy with its nearest neighbor atom is given by:N _(AA)=(½)N·Z·C _(A) ·P _(AA)

-   P_(AA): The probability that an A atom in an α sublattice and an A    atom in a β sublattice that constitute the alloy form A-A atom    pairs.-   Z: Coordination number-   P_(AA) is approximated as follows: $p_{A}^{i} = \begin{Bmatrix}    {1,} & {i \in \alpha} \\    {0,} & {i \in \beta}    \end{Bmatrix}$ $p_{A}^{j} = \begin{Bmatrix}    {1,} & {j \in \beta} \\    {0,} & {j \in \alpha}    \end{Bmatrix}$    (i = 1, 2, …  , N ⋅ c_(A), j = 1, 2, …  , N ⋅ (1 − c_(A))    -   p_(A) ^(i)(i ε α), p_(A) ^(j)(j ε β): The proportion at which A        atoms occupy α and β sublattice points $\begin{matrix}        {p_{AA} = {\frac{\frac{1}{2}N}{\frac{1}{2}{N \cdot c_{A} \cdot Z}}{\sum\limits_{i \neq j}{p_{A}^{i}p_{A}^{j}}}}} & & & & {( {{i \in \alpha},{j \in \beta}} )} \\        {= {\frac{1}{Z \cdot c_{A}}{\sum\limits_{i \neq j}{p_{A}^{i}p_{A}^{j}}}}} & & & &         \end{matrix}$        However, it is assumed that in the nearest neighbor atoms, there        is no correlation between an A-A atom pair formed by A atoms        within the same sublattice (ε_(AA)=0). Calculation conditions        related to the summation of the subscripts of the above equation        are as follows: $\quad\begin{Bmatrix}        {{{\sum\limits_{\alpha,\beta}p_{A}^{k}} = {{p_{A}^{\alpha} + p_{A}^{\beta}} = 1}}\quad} & {( {{k = \alpha},\beta} )\quad} \\        {{{\sum\limits_{i}p_{A}^{i}} = {{N_{\alpha} \cong N_{A}} = {N \cdot c_{A}}}}\quad} & ( {{i = 1},2,\ldots\quad,{N \cdot c_{A}},{i \in \alpha}}\quad  \\        {{\sum\limits_{i}p_{A}^{j}} = {{N_{\beta} \cong N_{\beta}} = {N \cdot ( {1 - c_{A}} )}}} & ( {{j = 1},\quad 2,\ldots\quad,{N \cdot ( {1 - c_{A}} )},}\quad  \\        \quad & { {{j \in \beta},{i \neq j}} )\quad} \\        {{{\sum\limits_{1}N_{1}} = {{N_{A} + N_{B}} = N}}\quad} & {( {{1 = \alpha},\beta} )\quad}        \end{Bmatrix}$

On the other hand, the relationship with the degree of long range orderS is expressed by the following equation:$S = {\frac{p_{A}^{\alpha} - c_{A}}{1 - v} = \frac{p_{A}^{\alpha} - c_{A}}{\gamma}}$However, from the relationship between C_(A) and ν (relativeconcentration of α sublattice), the value of γ is given by:γ=C _(A)(1−ν)/ν when C_(A)≦νγ=1−C _(A) when C_(A)≧νFrom these relationships the following equation stands:p _(A) ^(α) =S·γ+c _(A)

In the case of a B2-type ordered alloy, from the condition thatZ_(α)=Z_(β)=Z, the following equation is obtained:${p_{AA} = {{\frac{1}{{Zc}_{A}}\lbrack {\{ {{c_{A}Z_{\alpha}} + {( {1 - c_{A}} )Z_{\beta}}} \}( {c_{A} + {\gamma \cdot S}} ) \times ( {1 - c_{A} - {\gamma \cdot S}} )} \rbrack}\quad = {\frac{1}{c_{A}}( {c_{A} + {\gamma \cdot S}} ) \times ( {1 - c_{A} - {\gamma \cdot S}} )}}}\quad$${p_{AA} = {c_{A} - \frac{\gamma^{2}S^{2}}{c_{A}}}}\quad$

From the definition, the degree of short range order σ₁ holds:$\sigma_{1} = {{1 - \frac{p_{AB}}{c_{B}}} = {{1 - \frac{p_{BA}}{c_{A}}} = {{1 - \frac{1 - p_{BB}}{c_{A}}} = {1 - \frac{1 - p_{AA}}{c_{B}}}}}}$${{where}\quad\begin{Bmatrix}{{p_{AA} + p_{AB}} = 1} \\{{p_{BA} + p_{BB}} = 1} \\{{c_{A}p_{AB}} = {c_{B}p_{BA}}}\end{Bmatrix}}\quad$Therefore,

-   from σ=(P_(AA)−C_(A))/C_(B), the following equation is obtained:    σ₁=−γ² S ² /C _(A)(1−C _(A))  (Equation 5)

According to the present invention, the degree of long range order(degree of short range order) is calculated by substituting an R-valuefound from irradiation conditions and the degree of long range order inan equilibrium state and it is possible to predict an irradiated statefrom the value of the degree of long range order (degree of short rangeorder) The relationship between the degree of long range order (degreeof short range order) and the R-value (an irradiated state diagram) isshown in FIG. 1. Because the R-value is a function of damage rate φ andK-value (R=K/εφ) and the K-value is a function of irradiationtemperature T, it follows that the R-value becomes a function of damagerate φ and irradiation temperature T. The upper half of FIG. 1 shows, asa function of R, the first threshold value S_(th1) at which the degreeof long range order begins to decrease greatly under irradiation, whichis found from Equation 2, the second threshold value S_(th2) at whichthe degree of long range order almost reaches equilibrium after thedecrease, which is found from Equation 3, and the degree of long rangeorder in an equilibrium state Seq, which is found from Equation 4. Thelower half of FIG. 1 shows the degrees of short range order by Equation5 from each of the degrees of long range order.

A judgment method using the irradiated state diagram of FIG. 1 is asfollows. The R-value is calculated from a specific irradiation conditionrelated to a new material to be used and the S-value of the degree oflong range order found from Equation 1 is described within FIG. 1. Acomparison is made between the S-value and the S_(th1)-value, theS_(th2)-value and the S_(eq)-value, respectively, at the same R-value(where, 0≦S_(eq)<S_(th2)<S_(th1)<1), and from a magnitude relation ofthese values judgments are made in a qualitative manner as follows:

-   (1) When S_(th1)<S: the new material to be used is in an ordered    state and has a low damage level (the degree of long range order is    large);-   (2) When S_(th2)<S<S_(th1): the new material is in a transition    process from an ordered state to a disordered state and its damage    level fluctuates greatly and tends to increase rapidly (the degree    of long range order decreases substantially);-   (3) When S_(eq)<S<S_(th2): the new material is in a process of    almost reaching a disordered state and its damage level is large but    little fluctuates (the amount of a decrease in the degree of long    range order is small and the degree of long range order is small)    and;-   (4) When S<S_(eq): the new material is in a disordered state and has    a high damage level (the degree of long range order is small).

Also, from the degree of short range order in FIG. 1 it is possible tojudge local information, such as the tendency of a pair of dissimilaratoms (σ: a negative value) or a pair of atoms of the same kind (σ: apositive value) relating to the nearest neighbor atoms.

As shown in FIG. 1, the curves related to the degree of long range orderand the degree of short range order spread greatly vertically and it isexpected that in a material in which the degree of order comes veryclose to ±1, deterioration in properties under irradiation is small. InFIG. 1, various irradiation conditions are converted to the R-value thatis simple and changes predicted with respect to the degree of order aremade visible via the R-value (as a function of the R-value), therebymaking it possible to spatially grasp the behavior of these changes. Asa result of this, it becomes easy to make a comparison with variouschanges in physical properties and relations to these can be easilyfound.

Table 1 shows the relationship between the threshold values of thedegree of long range order and those of the degree of short range order.Degree of short range order of Warren-Cowley Degree of long range orderof σ₁ (between the nearest neighbor Bragg-Williams S atoms) EquilibriumEquilibrium value Threshold value value Threshold value S_(eq) S_(th2)S_(th1) σ_(1-eq) σ_(1-th2) σ_(1-th1) 0.1 0.197 0.351 −0.01 −0.039 −0.1230.2 0.385 0.598 −0.04 −0.148 −0.358 0.3 0.550 0.757 −0.09 −0.303 −0.5730.4 0.690 0.857 −0.16 −0.476 −0.734 0.5 0.800 0.918 −0.25 −0.64 −0.8430.6 0.882 0.956 −0.66 −0.778 −0.914 0.7 0.940 0.979 −0.49 −0.884 −0.9580.8 0.976 0.992 −0.64 −0.953 −0.984 0.9 0.994 0.998 −0.81 −0.988 −0.9960.92 0.997 0.999 −0.846 −0.994 −0.998 0.95 0.999 0.999 −0.998 −0.998−0.998 0.98 0.999 0.999 −0.998 −0.998 −0.998 0.99 0.999 0.999 −0.998−0.998 −0.998

The R-value (R=K/εφ=S_(eq)/(1−S_(eq))²: (0≦R<∞)) is found by determiningthe S_(eq)-value, and if the R-value is determined, the S_(th1)-valueand the S_(th2)-value are found from Equations 2 and 3, since each ofS_(th1)- and S_(th2)-values is a function of R. On the other hand, thedegree of short range order is found from the obtained degree of longrange order by using Equation 5, and σ_(eq)-value, the σ_(th1)-value andthe σ_(th2)-value are obtained from the S_(eq)-value, the S_(th1)-valueand the S_(th2)-value, respectively. Table 1 shows the results obtainedin this manner.

From the results of Table 1, it is apparent that in a case where anequilibrium value of the degree of long range order is close to 0.1 to0.2, for example, (which corresponds to a state in which disordering isremarkable), the extent to which the degree of order begins to lower,S_(th1), begins to decrease abruptly from 0.6, almost approachesequilibrium at 0.39 or so and reaches 0.2 (equilibrium value). Also,when the degree of order begins to decrease from 0.35 or so, S_(th1)almost approaches equilibrium at 0.2, and reaches equilibrium at 0.1. Ifthis degree of order that begins to lower, S_(th1), has large values of0.9 to 0.8 or so, then a decrease in the degree of order can besuppressed to 0.8 (equilibrium value: 0.5) to 0.6 (equilibrium value: alittle less than 0.4) even if the degree of order decreases (disorderingdoes not occur) In contrast, if the S_(th1)-value becomes not more than0.6, the degree of long range order decreases abruptly and it followsthat disordering becomes remarkable.

In response to these changes, the degree of short range order isobtained by squaring the degree of long range order, multiplying thisvalue by a coefficient, and reversing the symbol of the value.Therefore, in a case where an equilibrium value of the degree of longrange order is close to 0.1 to 0.2, an equilibrium value of the shortrange order shows −0.01 to −0.04 and becomes a value that is almostclose to zero (disordering). On the other hand, in a case where anequilibrium value of the degree of long range order is close to 0.9 to0.8, an equilibrium value of the short range order is −0.8 to −0.6 andthis shows that the ordering of short range order (the ordering of pairsof dissimilar atoms) has proceeded even at an atomic level.

As to a difference between the degree of long range order and the degreeof short range order, the degree to which the degree of order lowers islarger in the degree of short range order than in the degree of longrange order, and this suggests that even when a decrease in the degreeof order at a long range order level is small in the degree of longrange order, there may be a case where a decrease in the degree of shortrange order has more proceeded when viewed in terms of a change in thedegree of short range order at an atomic level.

The degree of short range order is a degree of order within the range ofan atomic level of the first neighbor atom, the second neighbor atom andthe third neighbor atom, i.e., within the nearest atom, the nearestneighbor atom second to this nearest atom and the nearest neighbor atomnext to this next neighbor atom (in Table 1, only cases between thenearest neighbor atoms are shown). In contrast, the degree of long rangeorder corresponds to a degree of order within a relatively large rangefrom several to tens of crystal lattices, and not an atomic level. Therelationship shown by Equation 5 exists between both degrees of order.In Equation 5, the degree of short range order is obtained bymultiplying a square of the degree of long range order by a constant andreversing the symbol of the value. By way of example, when the degree oflong range order approaches 1, the degree of short range orderapproaches −1 (pairs of dissimilar atoms).

The relationship between the degree of short range order and the degreeof long range order is as follows. In terms of the degree of long rangeorder, the closer to 1 the value, the larger the extent of ordering,whereas the closer to 0 the value, the higher the extent of disordering.In terms of the degree of short range order, the ordering of dissimilaratoms occurs when the value is close to −1 and the ordering of atoms ofthe same kind occurs when the value is close to +1, whereas disorderingoccurs when the value is close to 0. When an actual process ofirradiation damage is considered, irradiation damage occurs first to anextent that high-energy particles (neutrons, ions, electrons, etc.)collide against a material, thereby producing irradiation defects offine level (a level of the degree of short range order), theseirradiation defects then grow and coalesce, forming large aggregates ofdefects (a level of the degree of long range order) and finally leadingto cracks and breakages. The degree of short range order is more than anauxiliary judgment material and indispensable for making judgments at afine level in the initial stage of the damage process. In actual cases,after the judgment on the damage state of a whole sample by use of thedegree of long range order, a local damage state is verified by thedegree of short range order. In this sense, it is appropriate toconsider that the degree of short range order is used in makingjudgments in a “complementary” manner rather than in an “auxiliary”manner.

The relationship between temperature T and damage rate (damage speed) φis given by the following equation:${{- \frac{E}{kT}} - {\frac{1}{2}\ln\quad\phi}} = {{\ln\quad R} + {\ln\frac{{ɛ( {z\quad{\mathcal{v}}} )}^{\frac{1}{2}}}{{( {Z_{\alpha} + Z_{\beta} - 2} ) \cdot C_{A}}C_{B}}}}$The relationship between damage rate (damage speed) and temperature whenthe degree of long range order reaches equilibrium is as follows:${{\ln\quad\phi_{eq}} = {{{- \frac{2E}{{kT}_{eq}}} - {2\lfloor {{\ln\quad R} + {\ln\{ \frac{{ɛ( {z\quad{\mathcal{v}}} )}^{\frac{1}{2}}}{( {Z_{\alpha} + Z_{\beta} - 2} )C_{A}C_{B}} \}}} \rbrack}} = {{- \frac{2E}{{kT}_{eq}}} - {2\ln\frac{R \cdot {ɛ( {z\quad{\mathcal{v}}} )}^{\frac{1}{2}}}{( {Z_{\alpha} + Z_{\beta} - 2} )C_{A}C_{B}}}}}}\quad$where, T_(eq) denotes a temperature at which the degree of long rangeorder reaches equilibrium. Similarly, the following equation isobtained: $\begin{matrix}{{\ln\quad\phi_{th2}} = {{- \frac{2E}{{kT}_{th2}}} - {2\quad\ln\frac{{ɛ( {z\quad{\mathcal{v}}} )}^{\frac{1}{2}}}{( {Z_{\alpha} + Z_{\beta} - 2} )C_{A}C_{B}}} -}} \\{2\quad\ln\frac{S_{th2}}{2( {1 - S_{th2}} )}} \\{{\ln\quad\phi_{th1}} = {{- \frac{2E}{{kT}_{th1}}} - {2\quad\ln\frac{{ɛ( {z\quad{\mathcal{v}}} )}^{\frac{1}{2}}}{( {Z_{\alpha} + Z_{\beta} - 2} )C_{A}C_{B}}} -}} \\{2\quad\ln\frac{( {4 - {3S_{th1}^{2}}} )^{\frac{1}{2}} + {3S_{th1}} - 2}{12( {1 - S_{th1}} )}}\end{matrix}$where, the T_(th1)- and T_(th2)-values and the φ_(th1)- andφ_(th2)-values denote, respectively, threshold-value temperatures andthreshold-value damage rates related to the degree of long range order.

FIG. 2 shows how to make judgments directly from irradiation conditions,and it shows the relationship between the logarithmic damage rate, whichis an actual irradiation condition, and a reciprocal of irradiationtemperature. Because the same equations as in FIG. 1 are used, thedegree of long range order S to be found is unique and the method ofFIG. 1 and the method of FIG. 2 are equivalent to each other incalculating the S-value. Although the degree of short range order shownin FIG. 1 is not shown in FIG. 2, a similar diagram is obtained bydescribing the degree of short range order found by using Equation 5 inthe drawing in the same manner as in FIG. 1, if necessary.

FIG. 2 provides convenience in that the S-value can be judged directlyfrom actual irradiation conditions without the calculation of theR-value. In this case, in predicting changes in the S-value, decipheringwork and the like are not easy compared to FIG. 1, because a spatialimage related to the prediction of the S-value is not directly obtainedand besides a logarithmic representation is used. However, judgments canbe easily made if one becomes skillful in line drawing work related tothe diagram and deciphering work. Incidentally, the straight lines inFIG. 2 tend to move to down left in the figure when a recovery fromdamage is made and they tend to move to top right when damage proceeds.

EXEMPLIFICATION

The present inventors conducted a neutron irradiation test related to aTiNi alloy, which is a B2-type ordered alloy, in Japan Materials TestingReactor (JMTR) of Japan Atomic Energy Research Institute. From theresults of the test, it became apparent that when changes in the degreeof long range order are evaluated from changes in the amount of decreasein transition temperature found from electric resistance measurement, adecrease in the degree of long range order by irradiation with neutronscan be suppressed by holding the irradiation temperature at a levelexceeding 520 K, thereby greatly improving the deterioration inproperties by irradiation, and that the method of the present inventionis valid also experimentally.

According to the present invention that uses an irradiated state diagramthus devised, it is possible to substantially shorten the periods ofenormous irradiation tests, post-irradiation examinations and analysisevaluations, long-period implementation of which has hitherto beenindispensable, and to simply and rapidly derive practical conditions foruse of an ordered alloy under irradiation. According to the presentinvention, in developing new materials that usually require developmentperiods of not less than 10 years, it is possible to shorten the periodsto not more than several years, i.e., to not more than ⅓ the periodshitherto been required, and the present inventors could have theprospect that the development of materials that withstand irradiationenvironments is possible at low cost.

1. A method of judging practical conditions for use of an ordered alloyunder irradiation environments, comprising the steps of: preparing anirradiated state diagram that expresses a relation of a degree of longrange order to a variable R of an irradiated state related to a damagerate and an irradiation temperature on the basis of an evaluationformula related to the effect of irradiation on an irradiated state ofan alloy according to an ordered structure of the alloy by using, asparameters, the first threshold value at which the degree of long rangeorder begins to decrease greatly under irradiation, the second thresholdvalue at which the degree of long range order almost reaches equilibriumafter the decrease, and the degree of long range order in an equilibriumstate; calculating a variable R of an irradiated state under irradiationconditions under which an alloy to be judged is to be used and findingan S-value of degree of long range order corresponding to the variableR; and finding and comparing the first threshold value S_(th1), thesecond threshold value S_(th2) and the degree of long range order in anequilibrium state S_(eq) at the same R-value, to thereby predict adamage level and a variation condition of the damage level and judge thepractical conditions for use.
 2. The method of judging practicalconditions for use of an ordered alloy under irradiation environmentsaccording to claim 1, wherein a comparison is made between the S-valueand the S_(th1)-value, the S_(th2)-value and the S_(eq)-value,respectively, at the same R-value (where, 0≦S_(eq)<S_(th2)<S_(th1)<1),and from a magnitude relation of these values judgments are made asfollows: (1) When S_(th1)<S: the alloy to be judged is in an orderedstate and has a low damage level (the degree of long range order islarge); (2) When S_(th2)<S<S_(th1): the alloy to be judged is in atransition process from an ordered state to a disordered state and itsdamage level fluctuates greatly and tends to increase rapidly (thedegree of long range order decreases substantially); (3) WhenS_(eq)<S<S_(th2): the alloy to be judged is in a process of almostreaching a disordered state and its damage level is large but littlefluctuates (the amount of a decrease in the degree of long range orderis small and the degree of long range order is small) and; (4) WhenS<S_(eq): the alloy to be judged is in a disordered state and has a highdamage level (the degree of long range order is small).
 3. A method ofjudging practical conditions for use of an ordered alloy underirradiation environments, comprising the steps of: preparing anirradiated state diagram that expresses a relation of a damage rate to areciprocal of an irradiation temperature on the basis of an evaluationformula related to the effect of irradiation on an irradiated state ofan alloy according to an ordered structure of the alloy by using, asparameters, the first threshold value at which the degree of long rangeorder begins to decrease greatly under irradiation, the second thresholdvalue at which the degree of long range order almost reaches equilibriumafter the decrease, and the degree of long range order in an equilibriumstate; calculating a reciprocal of an irradiation temperature of analloy to be judged under irradiation conditions under which the alloy isto be used and finding an S-value of degree of long range ordercorresponding to the reciprocal of the irradiation temperature; andfinding and comparing the first threshold value S_(th1), the secondthreshold value S_(th2) and the degree of long range order in anequilibrium state S_(eq) at the same reciprocal of the irradiationtemperature, to thereby predict a damage level and a variation conditionof the damage level and judge the practical conditions for use.
 4. Themethod of judging practical conditions for use of an ordered alloy underirradiation environments according to claim 3, wherein a comparison ismade between the S-value and the S_(th1)-value, the S_(th2)-value andthe S_(eq)-value, respectively, at the same reciprocal of an irradiationtemperature (where, 0≦S_(eq)<S_(th2)<S_(th1)<1), and from a magnituderelation of these values judgments are made as follows: (1) WhenS_(th1)<S: the alloy to be judged is in an ordered state and has a lowdamage level (the degree of long range order is large); (2) WhenS_(th2)<S<S_(th1): the alloy to be judged is in a transition processfrom an ordered state to a disordered state and its damage levelfluctuates greatly and tends to increase rapidly (the degree of longrange order decreases substantially); (3) When S_(eq)<S<S_(th2): thealloy to be judged is in a process of almost reaching a disordered stateand its damage level is large but little fluctuates (the amount of adecrease in the degree of long range order is small and the degree oflong range order is small) and; (4) When S<S_(eq): the alloy to bejudged is in a disordered state and has a high damage level (the degreeof long range order is small).